LCM of 204 and 343
69972 is the LCM of 204 and 343. The step-by-step solution using prime factors and special division methods is one of the simple methods to easily understand how to find what is the LCM of 204 and 343, provided along with the use cases of mathematics and real-world problems.
what is the lcm of 204 and 343?
lcm (204 343) = (?)
204 => 2 x 2 x 3 x 17
343 => 7 x 7 x 7
= 2 x 2 x 3 x 17 x 7 x 7 x 7
= 69972
lcm (204 and 343) = 69972
69972 is the LCM of 204 and 343.
where,
204 is a positive integer,
343 is a positive integer,
69972 is the LCM of 204 and 343,
There is no common factors of 204 and 343 in {2 x 2 x 3 x 17, 7 x 7 x 7},
{2 x 2 x 3 x 17 x 7 x 7 x 7} in {2 x 2 x 3 x 17, 7 x 7 x 7} are the uncommon factors of 204 and 343.
Use in Mathematics: LCM of 204 and 343
The below are some of the mathematical applications where lcm of 204 and 343 can be used:
- to find the least number which is exactly divisible by 204 and 343.
- to find the common denominator for two fractions having 204 and 343 as denominators in the unlike fractions addition or subtraction.
In the context of lcm real world problems, the lcm of 204 and 343 helps to find the exact time when two similar and recurring events with different time schedule happens together at the same time. For example, the real world problems involve lcm in situations to find at what time the bells A and B all toll together, if bell A tolls at 204 seconds and bell B tolls at 343 seconds repeatedly. The answer is that all bells A and B toll together at 69972 seconds for the first time, at 139944 seconds for the second time, at 209916 seconds for the third time and so on.
Important Notes: 204 and 343 lcm
The below are the important notes to be remembered while solving the lcm of 204 and 343:
- The common prime factors and the remaining prime factors of 204 and 343 should be multiplied to find the least common multiple of 204 and 343, when solving lcm by using prime factors method.
- The results of lcm of 204 and 343, and the lcm of 343 and 204 are identical, it means the order of given numbers in the lcm calculation doesn't affect the results.
How-to: What is the LCM of 204 and 343?
The below solved example with step by step work shows how to find what is the lcm of 204 and 343 by using prime factors method and division method.
Solved example using prime factors method:
What is the LCM of 204 and 343?
step 1
Address the input parameters, values and observe what to be found:
Input parameters and values:
A = 204
B = 343
What to be found:
find the lcm of 204 and 343
step 2 Find the prime factors of 204 and 343:
Prime factors of 204 = 2 x 2 x 3 x 17
Prime factors of 343 = 7 x 7 x 7
step 3Identify the repeated and non-repeated prime factors of 204 and 343:
Since there is no common factors between 204 and 343, multiplying the given numbers directly provides the LCM of
204 and 343.
= 204 x 343
= 69972
lcm(204 and 343) = 69972
Hence,
lcm of 204 and 343 is 69972
This special division method is one of the easiest ways to understand the entire calculation to find the LCM of 204 and 343.
step 1 Address the input parameters, values and observe what to be found:
Input parameters and values:
Integers: 204 and 343
What to be found:
lcm (204, 343) = ?
step 2 Arrange the given integers in the horizontal form with space or comma separated format:
204 and 343
step 3 Choose the divisor which divides each or most of the given integers (204 and 343), divide each integers separately and write down the quotient in the next line right under the respective integers. Bring down the integer to the next line if any integer in 204 and 343 is not divisible by the selected divisor; repeat the same process until all the integers are brought to 1 as like below:
| 2 | 204 | 343 |
| 2 | 102 | 343 |
| 3 | 51 | 343 |
| 7 | 17 | 343 |
| 7 | 17 | 49 |
| 7 | 17 | 7 |
| 17 | 17 | 1 |
| 1 | 1 |
step 4 Multiply the divisors to find the lcm of 204 and 343:
= 2 x 2 x 3 x 7 x 7 x 7 x 17
= 69972
LCM(204, 343) = 69972
The LCM of two numbers 204 and 343 is 69972